Engineering programmable spin interactions in a trapped ion quantum simulator with holographic single-ion addressing*

Trapped ions are an ideal platform for quantum simulation of many-body spin Hamiltonians. To engineer arbitrary spin-spin interaction graphs, we need arbitrary addressing of individual spins. Here, we demonstrate holographic beam shaping using a digital micro-mirror device (DMD) for individually manipulating Yb+ ion spins and interactions between spin pairs. A precise optical intensity gradient will allow us to control individual spin phases, which can modify global Molmer-Sorensen interactions to realize the target interaction graph, in a hybrid analog-digital quantum simulation. This method of individual addressing is a scalable alternative for a long inhomogeneously spaced ion chain compared to other approaches that rely on scanning a tightly focused laser beam, or on devices that produce a fixed number of equally spaced laser beams.